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Joined: 30 Aug 2015
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GMAT 1: 570 Q47 V23 GMAT 2: 570 Q42 V27 GMAT 3: 680 Q50 V35 The cost C, in dollars of producing x units of a certain commodity is  [#permalink]

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The cost C, in dollars of producing x units of a certain commodity is given by the formula C(x) = 10.000 + bx + ax^2 where a, and b are constants. What is the value of a?

(1) The cost of producing 500 units is $15.833. (2) The cost of producing 1,000 units is twice the cost of producing 500 units. Originally posted by inakihernandez on 24 Apr 2016, 10:20. Last edited by Vyshak on 24 Apr 2016, 11:36, edited 1 time in total. Edited the url Most Helpful Expert Reply Math Expert V Joined: 02 Aug 2009 Posts: 7971 The cost C, in dollars of producing x units of a certain commodity is [#permalink] Show Tags 12 7 inakihernandez wrote: The cost C, in dollars of producing x units of a certain commodity is given by the formula C(x) = 10.000 + bx + ax^2 where a, and b are constants. What is the value of a? (1) The cost of producing 500 units is$15.833.

(2) The cost of producing 1,000 units is twice the cost of producing 500 units.

Hi
the equation has got two constants a and b..

lets see the statements

(1) The cost of producing 500 units is $15.833. we have two constants a and b, and one equation Insuff (2) The cost of producing 1,000 units is twice the cost of producing 500 units here when you make two quation and equate them you will realize you can find answer.. $$C(1000) = 10.000 + b*1000 + a1000^2$$ .. $$C(500) = 10.000 + b*500 + a500^2$$ .. now $$C(1000) = 2* C(500)$$.. so $$10.000 + b*1000 + a1000^2 = 2( 10.000 + b*500 + a500^2 )$$.. $$10.000 + b*1000 + a1000^2 = 20.000 + b*1000 + 2*a*500^2$$ b will get cancelled and you can find value of a.. Suff Hope it helps _________________ General Discussion EMPOWERgmat Instructor V Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 15263 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: The cost C, in dollars of producing x units of a certain commodity is [#permalink] Show Tags 2 Hi inakihernandez, You should post this question in the DS sub-Forum here: gmat-data-sufficiency-ds-141/ GMAT assassins aren't born, they're made, Rich _________________ Marshall & McDonough Moderator D Joined: 13 Apr 2015 Posts: 1685 Location: India Re: The cost C, in dollars of producing x units of a certain commodity is [#permalink] Show Tags 2 2 C(x) = 10.000 + bx + ax^2 a = ? St1: C(500) = 10 + 500b + a(25*10^4 ) = 15.833 We have 2 unknowns and hence value of 'a' cannot be determined without knowing the value of 'b' Not Sufficient St2: C(1000) = 2*C(500) 10 + 1000b + a(10^6) = 20 + 1000b + a(50*10^4) a(10^6 - 5*10^5) = 10 Sufficient to determine the value of 'a' Answer: B Senior Manager  Joined: 11 Nov 2014 Posts: 315 Location: India Concentration: Finance, International Business WE: Project Management (Telecommunications) Re: The cost C, in dollars of producing x units of a certain commodity is [#permalink] Show Tags 1 Vyshak wrote: C(x) = 10.000 + bx + ax^2 a = ? St1: C(500) = 10 + 500b + a(25*10^4 ) = 15.833 We have 2 unknowns and hence value of 'a' cannot be determined without knowing the value of 'b' Not Sufficient St2: C(1000) = 2*C(500) 10 + 1000b + a(10^6) = 20 + 1000b + a(50*10^4) a(10^6 - 5*10^5) = 10 Sufficient to determine the value of 'a' Answer: B how did you get this? a(25*10^4 ) a(50*10^4) Marshall & McDonough Moderator D Joined: 13 Apr 2015 Posts: 1685 Location: India Re: The cost C, in dollars of producing x units of a certain commodity is [#permalink] Show Tags 1 paidlukkha wrote: Vyshak wrote: C(x) = 10.000 + bx + ax^2 a = ? St1: C(500) = 10 + 500b + a(25*10^4 ) = 15.833 We have 2 unknowns and hence value of 'a' cannot be determined without knowing the value of 'b' Not Sufficient St2: C(1000) = 2*C(500) 10 + 1000b + a(10^6) = 20 + 1000b + a(50*10^4) a(10^6 - 5*10^5) = 10 Sufficient to determine the value of 'a' Answer: B how did you get this? a(25*10^4 ) a(50*10^4) Hi, I have skipped some multiplication steps in my explanation. x = 5*10^2 --> x^2 = 25*10^4 2*C(500) --> 2(10 + 500b + 25*10^4) --> 20 + 1000b + 2*25*10^4 Veritas Prep GMAT Instructor V Joined: 16 Oct 2010 Posts: 9705 Location: Pune, India Re: The cost C, in dollars of producing x units of a certain commodity is [#permalink] Show Tags 8 inakihernandez wrote: The cost C, in dollars of producing x units of a certain commodity is given by the formula C(x) = 10.000 + bx + ax^2 where a, and b are constants. What is the value of a? (1) The cost of producing 500 units is$15.833.

(2) The cost of producing 1,000 units is twice the cost of producing 500 units.

Let me point out here that this is a (C) trap question. The first statement will give an equation in a and b. So we know that we cannot find the value of a. When we look at the second statement, we see another equation in a and b which is not a multiple of the first equation and suddenly, it seems that we will be able to solve both equations simultaneously and get the answer. So (C) seems to be correct. But that is just too easy. Beware of the (C) trap. This should make you think - can I solve the question using a single statement alone. Make the equation of statement 2 since it gives you some convoluted relative data. When you do, you see that b gets canceled and in fact, you can get the value of a. Note that you cannot find the value of b from the second statement alone but the question doesn't ask for the value of b. We only need the value of a and hence second statement is sufficient alone.
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Current Student G
Joined: 28 Nov 2014
Posts: 818
Concentration: Strategy
Schools: Fisher '19 (M$) GPA: 3.71 Re: The cost C, in dollars of producing x units of a certain commodity is [#permalink] Show Tags The correct statement 1 is (1) The cost of producing 500 units of this commodity is$15833

It is NOT 15.833 although that won't affect the OA.
SVP  P
Joined: 03 Jun 2019
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Location: India
Re: The cost C, in dollars of producing x units of a certain commodity is  [#permalink]

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inakihernandez wrote:
The cost C, in dollars of producing x units of a certain commodity is given by the formula C(x) = 10.000 + bx + ax^2 where a, and b are constants. What is the value of a?

(1) The cost of producing 500 units is $15.833. (2) The cost of producing 1,000 units is twice the cost of producing 500 units. Given: The cost C, in dollars of producing x units of a certain commodity is given by the formula C(x) = 10.000 + bx + ax^2 where a, and b are constants. Asked: What is the value of a? (1) The cost of producing 500 units is$15.833.
C(x) = 10.000 + bx + ax^2
x = 500
C(x) = $15.833 = 10 + 500b + 250000a Since there are 2 unknowns NOT SUFFICIENT (2) The cost of producing 1,000 units is twice the cost of producing 500 units. 10 + 1000b + 1000000a = 2(10 + 500b + 250000a) 1000000a = 10 + 500000a 500000a = 10 $$a = \frac{1}{50000}$$ SUFFICIENT IMO B _________________ "Success is not final; failure is not fatal: It is the courage to continue that counts." Please provide kudos if you like my post. Kudos encourage active discussions. My GMAT Resources: - Efficient Learning All you need to know about GMAT quant Tele: +91-11-40396815 Mobile : +91-9910661622 E-mail : kinshook.chaturvedi@gmail.com SVP  P Joined: 03 Jun 2019 Posts: 1699 Location: India Re: The cost C, in dollars of producing x units of a certain commodity is [#permalink] Show Tags inakihernandez wrote: The cost C, in dollars of producing x units of a certain commodity is given by the formula C(x) = 10.000 + bx + ax^2 where a, and b are constants. What is the value of a? (1) The cost of producing 500 units is$15.833.

(2) The cost of producing 1,000 units is twice the cost of producing 500 units.

Given: The cost C, in dollars of producing x units of a certain commodity is given by the formula C(x) = 10.000 + bx + ax^2 where a, and b are constants.

Asked: What is the value of a?

(1) The cost of producing 500 units is \$15.833.
15.833 = 10 + 500b + 25000a
Since b is unknown, a can not be found out
NOT SUFFICIENT

(2) The cost of producing 1,000 units is twice the cost of producing 500 units.
10 + 1000b + 1000000a = 2 (10 + 500b + 250000a)
10 + 1000b + 1000000a = 20 + 1000b + 500000a
10 = 500000a
a = 10/500000
SUFFICIENT

IMO B
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E-mail : kinshook.chaturvedi@gmail.com Re: The cost C, in dollars of producing x units of a certain commodity is   [#permalink] 08 Oct 2019, 10:34
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